The Prime Minister is against imposing statutory controls on the press and prefers a voluntary code overseen by an independent body.

But the Lib Dem leader and deputy PM has made it clear he does not think it will work without statutory backing – a view shared by Labour leader Ed Miliband and actor Hugh Grant, a leading member of Hacked Off, which has campaigned for tougher laws after the exposure of widespread mobile phone hacking by Murdoch journalists.

The coalition leaders are due to receive Lord Justice Leveson's report at lunchtime today and will meet tonight to try to thrash out a response. There is also likely to be a meeting of the rarely used coalition committee tomorrow to try to agree a joint approach.

But Downing Street sources say Clegg might take the extraordinary step of making a separate statement to the Commons tomorrow - after Cameron - disagreeing with the Prime Minister. Clegg privately told members of Hacked Off back in September that there was nothing in the Coalition Agreement that prevented him from taking a different position on press regulation from the Conservatives.

Both Clegg and Miliband believe newspapers have been given enough "last chances" and that new regulation must be underpinned by law – a line the great British public apparently agrees with.

A YouGov poll for the Media Standards Trust shows 79 per cent in favour of an independent press regulator established by law. Only nine per cent were opposed.

Yet Cameron's aides are already talking about the Prime Minister taking the political heat by refusing to implement Leveson report if the judge recommends statutory controls.

The Tory party is deeply split over the issue. A total of 86 Tory peers and MPs have signed a letter to The Daily Telegraph and The Guardian opposing statutory controls. They include Liam Fox, David Davis, John Whittingdale, chairman of the media select committee, and Downton Abbey creator Lord (Julian) Fellowes.

Education Secretary Michael Gove and London mayor Boris Johnson, both journalists at heart, have already spoken out against statutory controls, while Foreign Secretary William Hague has urged Cameron to "err on the side of freedom".

But many backbenchers – burned by having their expenses fiddling exposed by the press, and pressured by angry constituents who have had run-ins with the press – strongly favour legislation.

The Prime Minister is now considering a free vote in the House of Commons allowing MPs to follow their conscience over the issue when it is debated on Monday.